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**Kat-M** Let $\displaystyle R(z)$ be a rational function:$\displaystyle R(z)=p(z)/q(z)$ where $\displaystyle p$ and $\displaystyle q$ are holomorphic polynomials. Let $\displaystyle f$ be holomorphic on $\displaystyle C$\ $\displaystyle \{P_1, P_2,....,P_k \}$ and suppose $\displaystyle f$ has a pole at each of the points $\displaystyle P_1, P_2,....,P_k$. Finally assume that $\displaystyle |f(z)| \leq |R(z)|$ for all $\displaystyle z$ at which these functions are defined. Prove that $\displaystyle f$ is a constant multiple of $\displaystyle R$.